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DOI: 10.4230/LIPIcs.FSTTCS.2009.2334

Deductive Verification of Continuous Dynamical Systems

Authors: Ankur Taly and Ashish Tiwari

Published in: LIPIcs, Volume 4, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)

Abstract

We define the notion of inductive invariants for continuous dynamical systems and use it to present inference rules for safety verification of polynomial continuous dynamical systems. We present two different sound and complete inference rules, but neither of these rules can be effectively applied. We then present several simpler and practical inference rules that are sound and relatively complete for different classes of inductive invariants. The simpler inference rules can be effectively checked when all involved sets are semi-algebraic.

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Ankur Taly and Ashish Tiwari. Deductive Verification of Continuous Dynamical Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 383-394, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{taly_et_al:LIPIcs.FSTTCS.2009.2334,
  author =	{Taly, Ankur and Tiwari, Ashish},
  title =	{{Deductive Verification of Continuous Dynamical Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{383--394},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Kannan, Ravi and Narayan Kumar, K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2334},
  URN =		{urn:nbn:de:0030-drops-23342},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2334},
  annote =	{Keywords: Deductive Verification, inductive invariants, continuous and hybrid dynamical systems, Theory of Reals}
}

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Deductive Verification of Continuous Dynamical Systems

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